In this appendix, we formulate the DFPCL method when observable confounders are present, building on [1]} and Mastouri and Zhu et al. [2]}. Here, we consider the causal graph given in Figure REF . In addition to variables \((A, Y, Z, W)\) , we have an observable confounder \(X \in \mathcal {X}\) . The structural function \(f_\mathrm {struct}\)  we aim to learn is

fstruct(a) = [X,U]Y A =a, X, U.
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